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Abstract

The aim of this thesis was to model blood pressure by using measurements from medical research. The available measurements contain the heart rate, systolic and diastolic pressure and cardiac output. We could show that the available data can be applied to basic models of the cardiovascular system. However, for improving the models and the estimation of their unknown parameters, we would need additional pressure measurements.

The thesis presents linear forward models, where the parameters were derived from physical conditions. Further, the thesis introduces a very general tool of inverse modeling, that can be applied in future research. The inverse modeling is based on the method of Lagrangian Multipliers with variational formulation. The computational implementation is accomplished with a symbolic finite elements tool, where the derivation of the Lagrangian equation and the preconditioner is automated. Due to its generality, the code for linear models could be applied to a nonlinear model with minor changes.

In spite of the few available measurements of pressure, forward and inverse modeling of the basic linear model gave similar results.